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The Physics of Double Jumping

By Salar Cheema

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Introduction

  • Double Jumping is the concept of jumping off the air again mid-jump
  • Analyzing Mario from Super Smash Bros
  • How fast does Mario need to kick his legs to double jump?
  • How much force does Mario kick with?
  • Is it possible to double jump in real life?
  • I will then explore the implications of Mario’s strength

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Video

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Plan

The main physics concept used is momentum because Mario’s legs collide with the air he pushes off of

  1. Find mario’s height and weight
  2. Find mario’s upwards velocity after his double jump by seeing how high he jumps
  3. Find the mass of the air
  4. Use conservation of momentum to solve for velocity of air
  5. Use F=J/t to solve for force of kick

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Data Collection

  • Mario’s weight: 25 kg
  • Mario’s height: 1 meter

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Data Collection

  • Mario’s double jump height: 2.5 m

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Methodology

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We want to solve for vair

We have Mario’s mass and velocity

But we don’t have the mass of the air

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Methodology

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Density of air is 1.225 kg/m3

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Volume is the column of air pushed away by mario’s feet (calculated by finding the surface area of Mario’s feet * the distance his legs extend)

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Methodology

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Methodology pt. 2

We can find force using the fact that it is equal to the change of momentum over time (Δp/t), but we need to find time first

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Results

Mario’s kick velocity: 14,628.57 m/s

Mario’s kick force: 20,491,800 N

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Conclusion

  • Fastest someone has ever kicked is 35.8 m/s, so double jumping is impossible in real life

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  • If upwards displacement after double jump is 0.01 m instead of 2.5 m, the velocity required is 450 m/s, so still impossible

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  • Escape velocity is only 11,184 m/s on Earth, so Mario could launch himself into orbit

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Conclusion pt. 2

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We can then use this velocity to find the most massive object that Mario can kick around the world

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Citations

“Mario.” Character Profile Wikia, characterprofile.fandom.com/wiki/Mario.

“Super Smash Bros. Accurate Heights by Sesshowmall on DeviantArt.” By Sesshowmall on DeviantArt, www.deviantart.com/sesshowmall/art/Super-Smash-Bros-Accurate-Heights-802648107.

Writer, Staff. “How Fast Can The Average Person Kick? – Fully Explained Here.” MMACHANNEL, MMACHANNEL, 19 Oct. 2021, mmachannel.com/how-fast-can-the-average-person-kick-fully-explained-here/.